ON z-SUBMODULES OF MODULES OVER C(X)

Abstract

Let R be a commutative ring with identity. As a generalization of z -ideals, a proper submodule N of an R-module M is a z-submodule if for any x 2 M and y 2 N that x belongs to the intersection of maximal submodule of M containing y, we have x 2 N. In this article, we give analogs of some well-known results about z -ideals of the ring of real-valued continuous functions C(X) (where X is a completely regular Hausdor space) in the context of modules over C(X).